SAMPLE TEST PAPER-1 - ALLEN

ALLEN

This Booklet contains 32 pages. 32 Do not open this Test Booklet until you are asked to do so.

Read carefully the Instructions on this Test Booklet.

Paper : Physics, Chemistry &

Mathematics

:

Important Instructions :

1. Immediately fill in the form number on this page of the Test Booklet with Blue/Black Ball Point Pen. Use of pencil is strictly prohibited.

2. The candidates should not write their Form Number

anywhere else (except in the specified space) on the Test

Booklet/Answer Sheet.

3. The test is of 3 hours duration. 4. The Test Booklet consists of 90 questions. The

maximum marks are 300. 5. There are three parts in the question paper 1, 2, 3

consisting of Physics, Chemistry and Mathematics having 30 questions in each subject and each subject having Two sections.

(i) Section-I contains 20 multiple choice questions

with only one correct option.

Marking scheme : +4 for correct answer and 0 if

not Attempted and –1 in all other cases.

(ii) Section-II contains 10 Numerical Value Type

questions. Attempt any 5 questions. First 5 attempted

questions will be considered for marking.

Marking scheme : +4 for correct answer and 0 in

all other cases.

6. Use Blue/Black Ball Point Pen only for writting

particulars/marking responses on Side–1 and Side–2 of

the Answer Sheet. Use of pencil is strictly prohibited.

7. No candidate is allowed to carry any textual material,

printed or written, bits of papers, mobile phone any

electronic device etc, except the Identity Card inside the

examination hall/room.

8. Rough work is to be done on the space provided for this purpose in the Test Booklet only.

9. On completion of the test, the candidate must hand over the Answer Sheet to the invigilator on duty in the Room/Hall. However, the candidate are allowed to take away this Test Booklet with them.

10. Do not fold or make any stray marks on the

Answer Sheet.

: 1.

2.

3. 3

4. 90 300

5. 1, 2, 3

30

2

(i) -I 20

: +4 0

–1

(ii) -II 10

5

: +4 0

6. –1 –2

7.

8.

9.

10.

Name of the Candidate (in Capitals) __________________________________________________________________________

( ) :

Form Number : in figures _______________________________________________________________________________

:

: in words ________________________________________________________________________________

:

Centre of Examination (in Capitals) : _________________________________________________________________________

( ) :

Candidate’s Signature : _______________________________ Invigilator’s Signature : _______________________________

: :

Your Target is to secure Good Rank in JEE(Main) 2021

Page 1/32

JEE(MAIN) : LEADER COURSE

(Academic Session : 2020 - 2021)

Test Pattern

SAMPLE TEST PAPER-1

JEE(Main)

ALLEN

Page2/32 SPACE FOR ROUGH WORK / Sample Test Paper-1

This section contains questions.

Each question has options (A), (B), (C)

and (D). of these four options is

correct.

For each question, darken the bubble corresponding

to the correct option in the ORS.

For each question, marks will be awarded in one

of the following categories :

Full Marks : +4 If only the bubble corresponding

to the correct option is darkened.

Zero Marks : 0 If none of the bubbles is darkened.

Negative Marks : –1 In all other cases

A car starts from rest, accelerates uniformly for 4 s

and then moves with uniform velocity. Which of

the following displacement-time graph represents

the motion of the car upto 7 s ?

(A) (B)

(C) (D)

4 7

s

0t

4 7

s

0t

4 7

s

0t

4 7

s

0t

PART 1 - PHYSICS

(A), (B), (C)

(D)

: +4

: 0

: –1

4

7 ?

(A) (B)

(C) (D)

4 7

s

0t

4 7

s

0t

4 7

s

0t

4 7

s

0t

ALLEN

Sample Test Paper-1 SPACE FOR ROUGH WORK / Page3/32

A stoner of mass 1 kg tied to a light inextensible

string of length 10/3 m is whirling in a circular

path of radius 10/3 m in a vertical plane. If the

ratio of the maximum tension in the string to the

minimum tension in the string is 4, the speed of the

stone at the highest point of the circle is :-

(Take g = 10 m/s2)

(A) 20 m/s (B) 15 m/s

(C) 10 m/s (D) 10 3 m/s

A particle which is constrained to move along the

x-axis, is subjected to a force in the same direction

which varies with the distance x of the particle

from the origin as F(x) = –kx + ax3.

Here k and a

are positive constants. For x 0, the functional

form of the potential energy U(x) of the particle is :

(A) (B)

(C) (D)

A disc has mass 9m. A hole of radius R/3 is cut

from it as shown in the figure. The moment of

inertia of remaining part about an axis passing

through the centre 'O' of the disc and perpendicular

to the plane of the disc is:

(A) 8 mR2 (B) 4 mR

2

(C) 40

9 mR

2 (D)

37

9 mR

2

U(x)

x

U(x)

x

U(x)

x

U(x)

x

R/3

OR

2R/3

10/3 1

10/3

4

:- (Take g = 10 m/s2)

(A) 20 m/s (B) 15 m/s

(C) 10 m/s (D) 10 m/s

x-

x

F(x) = –kx + ax3

k a x 0

U(x) :-

(A) (B)

(C) (D)

9m R/3

O

(A) 8 mR2 (B) 4 mR

2

(C) 40

9 mR

2 (D)

37

9 mR

2

U(x)

x

U(x)

x

U(x)

x

U(x)

x

R/3

OR

2R/3

ALLEN


Shots are fired from the top of a tower and from its

bottom simultaneously at angles 30° and 60° as

shown. If horizontal distance of the point of

collision is at a distance 'a' from the tower then

height of tower h is :

30°

60°

u2

u1

h

a

(A) 2a

3

(B) a

3

(C) 2a (D) 4a

3

In the given figure for u = u0/3, find the height

from the ground at which the block leaves the

hemisphere. [where 0

gru

3 ]

r

u /30

O

h

A

(A) 19 r

9 (B)

19 r

27

(C) 10 r

9 (D)

55r

81

In the figure shown the force (F) on a particle is

plotted against its position 'x' from origin. Then

which of the following statement is correct. A

particle at :

F

O XX1 X2 X3

(A) x1 is in stable equilibrium

(B) x2 is in stable equilibrium

(C) x3 is in stable equilibrium

(D) None of these

30° 60°

'a'

h

30°

60°

u2

u1

h

a

(A) 2a

3

(B) a

3

(C) 2a (D) 4a

3

u = u0/3

- [0

gru

3 ]

r

u /30

O

h

A

(A) 19 r

9 (B)

19 r

27

(C) 10 r

9 (D)

55r

81

(F)

'x'

F

O XX1 X2 X3

(A) x1

(B) x2

(C) x3

(D)

ALLEN


Choose CORRECT statement :-

(A) Electron & proton which are accelerated

through same potential difference from rest

will have same de-broglie wavelength.

(B) Proton and particle which are accelerated

through same potential difference from rest

will have same de-broglie wavelength.

(C) Two particles having same kinetic energy must

have same de-broglie wavelength.

(D) Two particles having different momentum may

have same de-broglie wavelength.

( ) :-

(A)

(B)

–

(C)

(D)

ALLEN


An electric dipole antenna is kept at the origin. The

dipole is oriented along y-axis. As the antenna

radiates electromagnetic waves, at a point on

x-axis :-

(A) There is no electromagnetic wave.

(B) Electric field is along y-direction and magnetic

field is along z-direction.

(C) Electric field is along z-direction and magnetic

field is along y-direction

(D) Electric field is along x-direction and magnetic

field is along y-direction.

In circuit shown the barrier voltage of diode is

0.7 V. The match the physical quantities :-

(A) A Q ; B R ; C P ; D S

(B) A P ; B S ; C R ; D Q

(C) A P ; B S ; C Q ; D R

(D) A S ; B P ; C Q ; D R

R = 500L

R = 10F

20V Peak

Column-I Column-II

(A) Peak current in diode (in mA) (P) 37.8

(B)Peak voltage (in volts) at the

end of load(Q) 40.0

(C)Peak current (in mA) if diode

is ideal(R) 20.0

(D)Peak voltage (in volts) at the

ends of loads if diode is ideal(S) 18.9

y-

x-

(A)

(B) y-

z-

(C) z-

y-

(D) x-

y-

0.7 V

:-

(A) A Q ; B R ; C P ; D S

(B) A P ; B S ; C R ; D Q

(C) A P ; B S ; C Q ; D R

(D) A S ; B P ; C Q ; D R

R = 500L

R = 10F

20V Peak

-I -II

(A) (mA ) (P) 37.8

(B)( )

(Q) 40.0

(C) (mA )

(R) 20.0

(D) (S) 18.9

ALLEN


Which of the following circuits provides full-wave

rectification of an ac input?

(A)

(B)

(C)

(D)

A bar magnet is freely suspended in such a way

that, when it oscillates in the horizontal plane. It

makes 20 oscillations per minute at a place, where

dip angle is 30° and 15 oscillations per minute at a

place, where dip angle is 60°. Ratio of total earth's

magnetic field at these two places :-

(A) 9 3 :16

(B) 9 : 3

(C) 3 : 16

(D) 16 : 9 3

?

(A)

(B)

(C)

(D)

30° 20

60° 15

(A) 9 3 :16

(B) 9 : 3

(C) 3 : 16

(D) 16 : 9 3

ALLEN


The mutual inductance between a long straight

wire and a square loop of side a as shown in figure

will be :-

I

xa

a

a a

(A) 0a

2

n

x a

x

(B) 0a

4

n

x a

x

(C) 0an

x a

x

(D) 0a

2

n

a

x

In the circuit shown in the figure, neglecting

source resistance, the voltmeter and ammeter

readings will respectively be -

R=30 XL=25 XC=25

240V

A

V

(A) 0 V, 8 A (B) 150 V, 8 A

(C) 150 V, 3 A (D) 0 V, 3 A

A number of capacitors each of capacitance 1µF

and each one of which get punctured if a potential

difference just exceeding 500 volt is applied, are

provided. Then an arrangement suitable for giving

a capacitor of 2 µF across which 3000 volt may be

applied requires at least :-

(A) 18 component capacitors

(B) 36 component capacitors

(C) 72 component capacitors

(D) 144 component capacitors

a

I

xa

a

a a

(A) 0a

2

n

x a

x

(B) 0a

4

n

x a

x

(C) 0an

x a

x

(D) 0a

2

n

a

x

R=30 XL=25 XC=25

240V

A

V

(A) 0 V, 8 A (B) 150 V, 8 A

(C) 150 V, 3 A (D) 0 V, 3 A

1µF

500 V

2µF

3000 V

:-

(A) 18

(B) 36

(C) 72

(D) 144

ALLEN


An infinitely long hollow conducting cylinder with

inner radius R/2 and outer radius R carries a

uniform current density along its length. The

magnitude of the magnetic field,

B as a function

of the radial distance r from the axis is best

represented by :-

(A)

rR/2 R

|B|

(B)

rR/2 R

|B|

(C)

rR/2 R

|B|

(D)

rR/2 R

|B|

(hollow)

R/2 R

B r

(A)

rR/2 R

|B|

(B)

rR/2 R

|B|

(C)

rR/2 R

|B|

(D)

rR/2 R

|B|

ALLEN


In a Young’s double slit experiment, I is the

intensity at the central maximum and is the

fringe width. The intensity at a point P distance x

from the centre will be-

(A) I cos

(B) 4I cos²

(C) I cos²

(D) I /4 cos²

An observer can see through a pin-hole the top end

of a thin rod of height h, placed as shown in the

figure. The beaker height is 3h and its radius h.

When the beaker is filled with a liquid up to a

height 2h, he can see the lower end of the rod.

Then the refractive index of the liquid is–

(A) 5

2 (B)

5

2 (C)

3

2

(D) 3

2

/

/

//

/ / //

//

/

/

/

/

/

h

2h

3h

I

x

P

(A) I cos

(B) 4I cos²

(C) I cos²

(D) I /4 cos²

- h

3h

h 2h

–

(A) 5

2 (B)

5

2 (C)

3

2

(D) 3

2

/

// /

//

/

/

/

/

/

/

/

/

/

h

2h

3h

ALLEN


If pressure amplitude in a sound wave is increased

three times, then the percentage increase in the

intensity of wave will be-

(A) 900% (B) 800%

(C) 600% (D) 500%

This section contains Questions. Attempt any

five Questions. First five Questions Attempt will

be considered for marking.

The answer to each question is a

.

For each question, enter the correct numerical

value (If the numerical value has more than two

decimal places, the value to

decimal places; e.g. 6.25, 7.00, –0.33, –.30,

30.27, –127.30, if answer is 11.36777..... then both

11.36 and 11.37 will be correct) by darken the

corresponding bubbles in the ORS.

If answer is –77.25, 5.2 then fill

the bubbles as follows.

Answer to each question will be evaluated

according to the following marking scheme:

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

(A) 900% (B) 800%

(C) 600% (D) 500%

(NUMERICAL VALUE)

(truncate/round-off)

6.25, 7.00, –0.33, –.30, 30.27, –127.30,

11.36777..... 11.36 11.37

)

–77.25, 5.2

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

ALLEN


Full Marks : +4 If ONLY the correct numerical

value is entered as answer.

Zero Marks : 0 In all other cases.

A ball is hit by a batsman at an angle of 37° as

shown in figure. The man standing at P should run

at what minimum velocity so that he catches the

ball before it strikes the ground. Assume that

height of man is negligible in comparison to

maximum height of projectile. (in m/s)

A man is crossing a river flowing with velocity of

5 m/s. He reaches a point directly across the river

at a distance of 60 m in 5 sec. His velocity in still

water should be (in m/s)

A stone is projected from point P on the inclined

plane with velocity v0 = 10 m/s directed

perpendicular to the plane. The time taken by the

stone to strike the horizontal ground S is (Given

PO = = 10 meter) (in sec)

man

u =15 m/s

37°A

B

9 m

P

60 m

A

B

V =5 r

m/s

53°

v0

P

OS

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

: +4

(Numerical value)

: 0

37°

P

5 m/s

60 m

5 s

P

v0 = 10 m/s

S

( PO = = 10 m) (sec )

man

u =15 m/s

37°A

B

9 m

P

60 m

A

B

V =5 r

m/s

53°

v0

P

OS

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

ALLEN


A vertical U-tube of uniform inner cross section

contains mercury in both sides of its arms.

A glycerin (density = 1.3 g/cm3) column of length

10 cm is introduced into one of its arms. Oil

of density 0.8 gm/cm3 is poured into the other

arm until the upper surfaces of the oil and

glycerin are in the same horizontal level. Find the

length of the oil column, (in cm) (Density of

mercury = 13.6 g/cm3) :-

10 cmoil

Mercury

Gly

ceri

n h

In the network shown in fig. determine V0

(in volt) :-

15v V0

6k

The circumference of the second Bohr orbit of

electron in hydrogen atom is 600 nm. The potential

difference then x is that must be applied between

the plates so that the electrons have the de-Broglie

wave length corresponding in this circumference is

:

U-

( = 1.3 g/cm3) 10 cm

( 0.8 gm/cm3)

( )

( = 13.6 g/cm3) :-

10 cmoil

Mercury

Gly

ceri

n h

V0 (volt ) :-

15v V0

6k

600 nm

x :-

ALLEN


A sphere of radius R have volume charge density

given as

(r) = Kr for r < R

= 0 for r > R

If electric field at distance R

2 from centre is

0

KR

N.

Then N will be.

In the connection shown in the figure the

switch K is open and the capacitor is

uncharged. Then we close the switch and let

the capacitor charge up to the maximum and

open the switch again. Then

(Use the following data : V0=30 V, R

1=10 k,

R2=5 k.)

C

R1 R2

KV0

(i) the current through R1 be I

1 immediately

after closing the switch

(ii) the current through R2

be I2 a long time

after the switch was closed

(iii) the current through R2

be I3 immediately

after reopening the switch

Find the value of 1

2 3

I

I I (in ampere–1).

R

(r) = Kr, r < R

= 0, r > R

R

2

0

KR

N N

K

V0 = 30 V, R1=10 k, R2 = 5 k

C

R1 R2

KV0

(i) R1 I

1

(ii) R2

I2

(iii) R2

I3

1

2 3

I

I I (ampere–1 )

ALLEN


. In the figure shown a mass 1 kg is connected to a

string of mass per unit length 1.2 gm/m. Length of

string is 1 m and its other end is connected to the

top of a ceiling which is accelerating up with an

acceleration 2 m/s . A transverse pulse is produced

at the lowest point of string. Time taken (In sec) by

pulse to reach the top of string is :

A concave mirror has radius of curvature of 40 cm.

It is at the bottom of a glass that has water filled up

to 5 cm (see figure). If a small particle is floating

on the surface of water, its image as seen, from

directly above the glass, is at a distance 'd' cm from

the surface of water. The value of d is close to :

(Refractive index of water = 1.33)

1kg

1m

a=2m/s2

5cm

particle

. 1 kg

1.2 gm/m

1 m

2 m/s

(sec )

40 cm

( )

5 cm

d 'd'

( ) : ( = 1.33)

1kg

1m

a=2m/s2

5cm

particle

ALLEN





correct.









PART 2 - CHEMISTRY

(A), (B), (C)

(D)

: +4

: 0

: –1

ALLEN


ALLEN


Which of the following compound undergo aldol

condensation ?

(A) CHO (B)

CH3–C–CHO

CH3

CH3

(C)

O

O

(D)

CH—CH

O O

Which of the given following stability order is

correct?

(A)

H2C

O<

O

(B)

> O

(C)

> H2N CH2

(D)

Cl<

F

CH2 CH2

?

(A) CHO (B)

CH3–C–CHO

CH3

CH3

(C)

O

O

(D)

CH—CH

O O

(A)

H2C

O<

O

(B)

> O

(C)

> H2N CH2

(D)

Cl<

F

CH2 CH2

ALLEN


OH–

OH

+

NH2

N2 Cl

X; here X is :-

(A)

OH

NH2

NN

(B)

OH

NH2

N

N

(C)

OH

(D)

OH

N N

OH–

OH

+

NH2

N2 Cl

X; X :-

(A)

OH

NH2

NN

(B)

OH

NH2

N

N

(C)

OH

(D)

OH

N N

ALLEN


Which of the following is methyl--D-glucoside?

(i)

HO

OH

OH

OCH3

HOCH2

O

(ii) HOCH2

HO

OH

OH

OCH3O

(iii)

HO

OH

OH

OH

HOCH2 O

(iv)

HO

OH

OCH3

OH

HOCH2 O

(v)

HO

OH

OCH3

OHHOCH2 O

(A) (i) (B) (ii) (C) (iii) (D) (iv)

CH3–C

OH

O

Can be obtained as one of the product

in reaction :-

(A)

CH3–C

CH3

O(1) I2/OH

–

(2) H (B) CH3–C

H

OCH3CO3H

(C) CH3–CH=CH2

O3

H2O (D) All

--D- ?

(i)

HO

OH

OH

OCH3

HOCH2

O

(ii) HOCH2

HO

OH

OH

OCH3O

(iii)

HO

OH

OH

OH

HOCH2 O

(iv)

HO

OH

OCH3

OH

HOCH2 O

(v)

HO

OH

OCH3

OHHOCH2 O

(A) (i) (B) (ii) (C) (iii) (D) (iv)

CH3–C

OH

O

:-

(A)

CH3–C

CH3

O(1) I2/OH

–

(2) H (B) CH3–C

H

OCH3CO3H

(C) CH3–CH=CH2

O3

H2O (D)

ALLEN


Which of the following nitrogen atom is maximum

basic ?

H2N–C–NH–CH

3

(b)

(c)

NH (a)

(A) b (B) a (C) c (D) All are same

How many stereo isomers possible from pentane-

2,3,4- triol :-

NH

(A) 2 (B) 3

(C) 4 (D) 5

Match incorrect equivalent mass of reactant in

following column ? (M = molar mass of reactant):-

(A) FeS2 Fe

3+ + SO

3

M

15

(B) P2H

4 P

4H

2

+ PH

3

5M

6

(C) 2Mn+7 Mn

2+ + Mn

+6

M

3

(D) Ba(MnO4)

2

H

Mn

2+ M

5

At 25°C, Ksp

for PbBr2 is equal to 8 × 10

–5. If the

salt is 80% dissociated, what is the solubility of

PbBr2 in mol L

–1 ?

(A)

1/34

10

1.6 1.6

(B)

1/35

10

1.6 1.6

(C)

1/34

10

0.8 0.8

(D)

1/25

10

1.6 1.6

H2N–C–NH–CH

3

(b)

(c)

NH (a)

(A) b (B) a (C) c (D)

-2,3,4-

:-

NH

(A) 2 (B) 3

(C) 4 (D) 5

? (M = ):-

(A) FeS2 Fe

3+ + SO

3

M

15

(B) P2H

4 P

4H

2

+ PH

3

5M

6

(C) 2Mn+7 Mn

2+ + Mn

+6

M

3

(D) Ba(MnO4)

2

H

Mn

2+ M

5

25°C PbBr2 K

sp 8 × 10

–5

80% PbBr2

L–1

?

(A)

1/34

10

1.6 1.6

(B)

1/35

10

1.6 1.6

(C)

1/34

10

0.8 0.8

(D)

1/25

10

1.6 1.6

ALLEN


In fcc lattice, A, B, C and D atoms are arranged at

corner, face centre, octahedral void and tetrahedral

void respectively, then the body diagonal

contains :-

(A) 2A, C, 2D (B) 2A, 2B, 2C

(C) 2A, 2B, 2D (D) 2A, 2D

Two solutions S1 and S

2 containing 0.1 M NaCl

(aq) and 0.05 M BaCl2 (aq) are sparated by

semiperameable membrane.

Which among the following statement(s) is/are

correct ? (Assume complete dissociation of both

the electrolytes)

(A) S1 and S

2 are isotonic

(B) S1 is hypertonic while S

2 is hypotonic

(C) S1 is hypotonic while S

2 is hypertonic

(D) All the above

In the concentration cell,

Pt(H2)

H (0.1 ) H (1 )

Na (1 ) Na (1 )

A M A M

A M A M (H

2) Pt

(pKa of HA = 4)

Cell potential will be :-

(A) 0.03 V (B) 0.06 V

(C) – 0.06 V (D) – 0.03 V

S1

0.1MNaCl

S2

0.05MBaCl2

fcc , A, B, C D

:-

(A) 2A, C, 2D (B) 2A, 2B, 2C

(C) 2A, 2B, 2D (D) 2A, 2D

S1 S

2

0.1 M NaCl 0.05M BaCl2

( ) :-

(A) S1 S

2

(B) S1 S

2

(C) S1 S

2

(D)

-

Pt(H2)

H (0.1 ) H (1 )

Na (1 ) Na (1 )

A M A M

A M A M (H

2) Pt

pKa (HA) = 4 :-

(A) 0.03 V (B) 0.06 V

(C) – 0.06 V (D) – 0.03 V

S1

0.1MNaCl

S2

0.05MBaCl2

ALLEN


Which of the following statements are correct ?

a. The smaller the gold number of lyophilic

colloid, the larger will be its protective power.

b. Lyophilic sols, in contrast to lyophobic sols are

easily coagulated on addition of small amounts

of electrolytes.

c. Ferric chloride solution is used to stop bleeding

from a fresh cut because it coagulates the

blood.

d. The flocculation value of arsenious sulphide

sol is independent of the anion of the

coagulating electrolyte.

(A) a, b and c (B) a, c and d

(C) b, c and d (D) a, b and d





.








?

a.

b.

c. FeCl3

d. AS2S

3

(A) a, b c (B) a, c d

(C) b, c d (D) a, b d

(NUMERICAL VALUE)


6.25, 7.00, –0.33, –.30, 30.27, –127.30,

11.36777..... 11.36 11.37

)

ALLEN









Number of elements in the 4th period of the

periodic table is x and number of elements in

the 6th period is equal to y find (x + y) =

Sum of number of and bonds present in

P4O10 :-

One mole of N2 react with three mole of H2 to

give x mole of ammonia, find x = ?

Total number of stereoisomer :-

H

CH

CH

CH — CH

CH3

CH3

CH3B

CH CH2

C CH—CH3

CH—CH3

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

–77.25, 5.2

: +4

(Numerical value)

: 0

= x = y

(x + y)

P4O10

:-

N2 3 H2

x x

:-

H

CH

CH

CH — CH

CH3

CH3

CH3B

CH CH2

C CH—CH3

CH—CH3

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

ALLEN


Find the value of x? (x = mole of RMgX consumed).

OHO O

O

Cl

OEt

O

Number of optically active monochlorinated

product formed in following reaction :-

CH3 MonochlorinationProducts

Chlorine is prepared in the laboratory by treating

manganese dioxide (MnO2) with aqueous

hydrochloric acid according to the reaction

4HCl(aq) + MnO2(s) 2H

2O() + MnCl

2(aq) + Cl

2(g)

How many gram of HCl react with 5.0 g of

manganese dioxide ? (At. wt. of Mn = 55)

The enthalpy change for the reaction of 50 ml of

ethylene with 50.0 mL of H2 at 1.5 atm. pressure is

H = –0.31 KJ. What is the U?

The equilibrium constant for the esterification

reaction of acetic acid and ethyl alcohol at 100°C

is 4. What percentage of alcohol has been

esterified ?

A solution of N2O

5 in CCl

4 yields by

decomposition at 45ºC, 5 ml of O2, 20 minutes

after the start of the experiment and 10 ml of O2

after a very long time. The decomposition obeys I

order kinetics. What volume of O2

would have

evolved, 40 minutes after the start

x (x = RMgX

)

OHO O

O

Cl

OEt

O

CH3 MonochlorinationProducts

(MnO2) HCl

:

4HCl(aq) + MnO2(s) 2H

2O() + MnCl

2(aq) + Cl

2(g)

5.0 g HCl

(Mn = 55)

1.5 50.0 ml

50.0 ml H2

–0.31 KJ U ?

100°C

4

N2O

5 CCl

4 45ºC

20 5 ml O2

10 ml , O2

40 O2

:-

ALLEN





correct.









The number of solutions of the equation

tan2x – sec

10 x + 1 = 0 in (0, 10) is

(A) 3 (B) 6 (C) 10 (D) 0

Which of the following statements is a tautology?

(A) ~(p ~q) p q

(B) ~(p ~q) p q

(C) ~(p ~q) p q

(D) p (~q) p q

From a pack of 52 well shuflled cards, cards are

drawn one by one without replacement. If 4th

drawn card is found to be ace, then what is the

probability, that there are no more aces left in the

pack is :- :-

(A)48 49

3 2

1

C 3 C 1 (B)

48 49

3 2

1

C C 1

(C) 48 49

3 2

1

3 C C 1 (D)

52

4

1

C 1

PART 3 – MATHEMATICS

(A), (B), (C)

(D)

: +4

: 0

: –1

tan2x – sec

10 x + 1 = 0 (0, 10)

(A) 3 (B) 6 (C) 10 (D) 0

(A) ~(p ~q) p q

(B) ~(p ~q) p q

(C) ~(p ~q) p q

(D) p (~q) p q

4

:-

(A)48 49

3 2

1

C 3 C 1 (B)

48 49

3 2

1

C C 1

(C) 48 49

3 2

1

3 C C 1 (D)

52

4

1

C 1

ALLEN


If

2

2

2 2

1 1 (x y)

z z z

(y z) 1 1D

x x x

y(y z) x 2y z y(x y)

x z xz xz

then, the incorrect statement is -

(A) D is independent of x

(B) D is independent of y

(C) D is independent of z

(D) D is dependent on x, y, z

If z – 1

= 2z – 4

and w – 4

= 2w – 1

, then the value of

|z – w|max

+ |z – w|min

is -

(A) 8 (B) 9 (C) 10 (D) 11

If a2 + b

2 + c

2 = 0 and matrix

A =

2 2

2 2

2 2

b c ab ac

ab c a bc

ac bc a b

and if |adj(adjA)| = 32a8b

8c

8, (a, b, c 0), then

=

(A) 8 (B) 16 (C) 32 (D) 4

If 2a + 2b + 3c = 1

5 and a, b, c R

+, then

maximum value of term independent of x in the

expansion of (ab x1/2

+ cx–1/3

)25

is –

(A) 25

C10

(B) 25

C10

(35)25

(C) 25

C15

35

1

35

(D) None of these

2

2

2 2

1 1 (x y)

z z z

(y z) 1 1D

x x x

y(y z) x 2y z y(x y)

x z xz xz

:-

(A) D, x

(B) D, y

(C) D, z

(D) D, x, y, z

z – 1

= 2z – 4

w – 4= 2

w – 1

|z – w|max

+ |z – w|min

:-

(A) 8 (B) 9 (C) 10 (D) 11

a2 + b

2 + c

2 = 0

A =

2 2

2 2

2 2

b c ab ac

ab c a bc

ac bc a b

|adj(adjA)| = 32a8b

8c

8, (a, b, c 0)

:-

(A) 8 (B) 16 (C) 32 (D) 4

2a + 2b + 3c = 1

5 a, b, c R

+

(ab x1/2

+ cx–1/3

)25

x

–

(A) 25

C10

(B) 25

C10

(35)25

(C) 25

C15

35

1

35

(D)

ALLEN


If , are the roots of equation x2

– 2x + 5 = 0,

then equation, whose roots are

3 + 2

– + 22, 3 + 42

– 7+ 35 is :-

(A) x2 – 57x + 770 = 0

(B) x2 – 12x + 35

(C) x2 – 2x + 5 = 0

(D) x2 – 11x + 28 = 0

If the tangent to the curve y = x + sin y at a point

(a, b) is parallel to the line joining 3

0,2

and

1

, 22

, then

(A) |b – a| = 1 (B) |a + b| = 1

(C) b = a (D) b = 2

+ a

Let f(–1, ) R be defined by f(0) = 1 and

f(x) = 1

x loge(1 + x), x 0. Then the function f

(A) decreases in (–1, 0) and increases in (0, )

(B) increases in (–1, )

(C) increases in (–1, 0) and decreases in (0, )

(D) decreases in (–1, )

Let [t] denote the greatest integer t. If for some

R – {0, 1}, x 0

lim

1 x | x |

x [x] = L, then L is

equal to

(A) 1 (B) 2 (C) 1

2 (D) 0

x2

– 2x + 5 = 0 ,

3 + 2

– + 22, 3 + 42

– 7+ 35 :-

(A) x2 – 57x + 770 = 0

(B) x2 – 12x + 35

(C) x2 – 2x + 5 = 0

(D) x2 – 11x + 28 = 0

y = x + sin y (a, b)

30,

2

1

, 22

(A) |b – a| = 1 (B) |a + b| = 1

(C) b = a (D) b = 2

+ a

f(–1, ) R

f(0) = 1 f(x) = 1

x loge(1 + x), x 0. f

(A) (–1, 0) (0, )

(B) (–1, )

(C) (–1, 0) (0, )

(D) (–1, )

[t] t R – {0, 1},

x 0

lim

1 x | x |

x [x] = L, L

(A) 1 (B) 2 (C) 1

2 (D) 0

ALLEN


If the surface area of a cube in increasing at a rate

of 3.6 cm2/sec, retaining its shape; then the rate

of change of its volume (in cm3/sec), when the

length of a side of the cube is 10cm, is

(A) 18 (B) 10 (C) 9 (D) 20

Let f(x) = min. x 1, 1 x for all x 1. Then

the area bounded by y = f(x) and the x-axis is :-

(A) 7

3 sq. units (B)

1

6sq. units

(C) 11

6sq. units (D)

7

6sq. units

x

e (1 tan x)sec x dx equals :-

(A) e–x

sec x + c (B) e–x

tan x + c

(C) –e–x

tan x + c (D) x

e secx c

The general solution of differential equation,

sin2x

dytan x y 0

dx is

(A) y cot x tan x C (B) y cot x x C

(C) y tan x cot x C (D) y tan x x C

If y = 3x is a tangent to a circle with centre

(1, 1), then the other tangent drawn through

(0, 0) to the circle is :-

(A) 3y = x (B) y = –3x

(C) y = 2x (D) y = –2x

The vertex C of a triangle ABC is (4, –1). The

equation of altitude AD and Median AE are

2x – 3y + 12 = 0 and 2x + 3y = 0 respectively then

slope of side AB is :-

(A) 3

7 (B)

3

2

(C) 9

11 (D) None of these

3.6 cm2/sec

10 cm

(cm3/sec )

(A) 18 (B) 10 (C) 9 (D) 20

f(x) = min. x 1, 1 x ; x 1

y = f(x) x- :-

(A) 7

3 sq. units (B)

1

6sq. units

(C) 11

6sq. units (D)

7

6sq. units

x

e (1 tan x)sec x dx :-

(A) e–x

sec x + c (B) e–x

tan x + c

(C) –e–x

tan x + c (D) x

e secx c

sin2x

dytan x y 0

dx

(A) y cot x tan x C (B) y cot x x C

(C) y tan x cot x C (D) y tan x x C

y = 3x

(1, 1) ,

(0, 0) :-

(A) 3y = x (B) y = –3x

(C) y = 2x (D) y = –2x

ABC C (4, –1)

AD AE

2x – 3y + 12 = 0 2x + 3y = 0 AB

:-

(A) 3

7 (B)

3

2

(C) 9

11

(D)

ALLEN


The foci of a hyperbola lie at the vertices of the

ellipse

2 2x y

1100 64

and its directrixes pass

through the foci of the ellipse. The equation of the

hyperbola must be :-

(A)

2 2x y

1100 64

(B)

2 2x y

140 60

(C)

2 2x y

160 40

(D) None of these

Equation of the plane passing through the point

ˆ ˆ î j– 2k , ˆ ˆ ˆ2i – j k and ˆ ˆ î 2 j k is :-

(A) ˆ ˆr.(4i 2 j) 20

(B) ˆ ˆ ˆr.(9i 3 j k) 14

(C) ˆ ˆ ˆr.(9i 3 j k) 6

(D) None of these

The equation of the chord joining two points

(x1, y

1) and (x

2, y

2) on the rectangular hyperbola

xy = c2 is :-

(A)

1 2 1 2

x y+ = 1

x + x y + y (B)

1 2 1 2

x y+ = 1

x - x y - y

(C)

1 2 1 2

x y+ = 1

y + y x + x (D)

1 2 1 2

x y+ = 1

y - y x - x





.




2 2x y

1100 64

:-

(A)

2 2x y

1100 64

(B)

2 2x y

140 60

(C)

2 2x y

160 40

(D)

ˆ ˆ î j– 2k , ˆ ˆ ˆ2i – j k , ˆ ˆ î 2 j k

:-

(A) ˆ ˆr.(4i 2 j) 20

(B) ˆ ˆ ˆr.(9i 3 j k) 14

(C) ˆ ˆ ˆr.(9i 3 j k) 6

(D)

xy = c2 (x

1, y

1) (x

2, y

2)

:-

(A)

1 2 1 2

x y+ = 1

x + x y + y (B)

1 2 1 2

x y+ = 1

x - x y - y

(C)

1 2 1 2

x y+ = 1

y + y x + x (D)

1 2 1 2

x y+ = 1

y - y x - x

(NUMERICAL VALUE)


ALLEN













If the variance of first n natural no. is 10 and the

variance of first m odd natural no is if 16 then

n – m is :-

A man standing between two vertical posts finds

that the angle subtended at his eyes by the tops of

the posts is a right angle. If the heights of the two

posts are two times and four times the height of the

man and the distance between them is

x1, x

2 & x

3 when divided by 4 leaves a remainder

of 0, 1 & 2 respectively find number of

non-negative integral solution of the equation

x1 + x

2 + x

3 = 35, is –

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

6.25, 7.00, –0.33, –.30, 30.27, –127.30,

11.36777..... 11.36 11.37

)

–77.25, 5.2

: +4

(Numerical value)

: 0

n 10

m 16

n – m :-

x1, x

2 x

34

0, 1 2

x1 + x

2 + x

3 = 35

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

0 0 0

+

0

–

0 0

1 1 1 1 1 1

2 2 2 2 2 2

3 3 3 3 3 3

4 4 4 4 4 4

5 5 5 5 5 5

6 6 6 6 6 6

7 7 7 7 7 7

8 8 8 8 8 8

9 9 9 9 9 9

•

•

•

•

•

•

•

•

•

•

ALLEN


If x6 – 12x

5 + ax

4 – bx

3 + cx

2 – dx + 64 = 0 has all

positive real roots, then (a) is equal to

Suppose a differentiable function f(x) satisfies the

identity f(x + y) = f(x) + f(y) + xy2 + x

2y, for all

real x and y. If x 0

lim

f(x)

x = 1, then f(3) is equal

to…. .

Let f(x) = xx

2

, for –10 < x < 10, where [t]

denotes the greatest integer function. Then, the

number of points of discontinuity of f is equal to

… .

1

1

x [2x] dx equals :- ([.] GIF)

If

2

4

0

1dx (k N)

k1 tan x , then k equals

If a

and b

are non zero and non collinear vectors

such that x(a b) (sin )a (cos )b

, then

number of values of cos + sinis :-

Two lines are drawn through (3, 4), each of which

makes angle of 45° with the line x – y = 2, Then

area of the triangle formed by these lines is :-

x6 – 12x

5 + ax

4 – bx

3 + cx

2 – dx + 64 = 0

(a)

f(x), f(x + y) = f(x) +

f(y) + xy2 + x

2y x y

x 0

lim

f(x)

x = 1 f(3)

f(x) = xx

2

,–10 < x < 10, [t]

f

1

1

x [2x] dx :- ([.] )

2

4

0

1dx (k N)

k1 tan x, k

a

b

x(a b) (sin )a (cos )b

cos + sin :-

(3, 4),

x – y = 2 45°

:-

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